Question: Simplify the following expression and state the condition under which the simplification is valid: $p = \dfrac{x^2 + 9x}{x^2 + 2x - 63}$
Solution: First factor the expressions in the numerator and denominator. $ \dfrac{x^2 + 9x}{x^2 + 2x - 63} = \dfrac{(x)(x + 9)}{(x - 7)(x + 9)} $ Notice that the term $(x + 9)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(x + 9)$ gives: $p = \dfrac{x}{x - 7}$ Since we divided by $(x + 9)$, $x \neq -9$. $p = \dfrac{x}{x - 7}; \space x \neq -9$